Element removal design in microwave filters

ABSTRACT

A method of designing a microwave filter using a computerized filter optimizer, comprises generating a filter circuit design in process (DIP) comprising a plurality of circuit elements having a plurality of resonant elements and one or more non-resonant elements, optimizing the DIP by inputting the DIP into the computerized filter optimizer, determining that one of the plurality of circuit elements in the DIP is insignificant, removing the one insignificant circuit element from the DIP, deriving a final filter circuit design from the DIP, and manufacturing the microwave filter based on the final filter circuit design.

RELATED APPLICATION DATA

The present application is a continuation of U.S. application Ser. No.13/939,763, filed Jul. 11, 2013, which claims the benefit under 35U.S.C. § 119 to U.S. provisional patent application Ser. No. 61/802,114,filed Mar. 15, 2013, which applications are all incorporated herein byreference in their entirety.

FIELD OF THE INVENTION

The present inventions generally relate to microwave filters, and moreparticularly, to acoustic wave microwave filters designed fornarrow-band applications.

BACKGROUND OF THE INVENTION

Electrical filters have long been used in the processing of electricalsignals. In particular, such electrical filters are used to selectdesired electrical signal frequencies from an input signal by passingthe desired signal frequencies, while blocking or attenuating otherundesirable electrical signal frequencies. Filters may be classified insome general categories that include low-pass filters, high-passfilters, band-pass filters, and band-stop filters, indicative of thetype of frequencies that are selectively passed by the filter. Further,filters can be classified by type, such as Butterworth, Chebyshev,Inverse Chebyshev, and Elliptic, indicative of the type of bandshapefrequency response (frequency cutoff characteristics).

The type of filter used often depends upon the intended use. Incommunications applications, band pass and band stop filters areconventionally used in cellular base stations, cell phone handsets, andother telecommunications equipment to filter out or block RF signals inall but one or more predefined bands. Of most particular importance isthe frequency range from approximately 500-3,500 MHz.

With reference to FIG. 1 a prior art telecommunications system 10 mayinclude a transceiver 12 capable of transmitting and receiving wirelesssignals, and a controller/processor 14 capable of controlling thefunctions of the transceiver 12.

The transceiver 12 generally comprises a broadband antenna 16, aduplexer 18 having a transmit filter 24 and a receive filter 26, atransmitter 20 coupled to the antenna 16 via the transmit filter 24 ofthe duplexer 18, and a receiver 22 coupled to the antenna 16 via thereceive filter 26 of the duplexer 18.

The transmitter 20 includes an upconverter 28 configured for convertinga baseband signal provided by the controller/processor 14 to a radiofrequency (RF) signal, a variable gain amplifier (VGA) 30 configured foramplifying the RF signal, a bandpass filter 32 configured for outputtingthe RF signal at an operating frequency selected by thecontroller/processor 14, and a power amplifier 34 configured foramplifying the filtered RF signal, which is then provided to the antenna16 via the transmit filter 24 of the duplexer 18.

The receiver 22 includes a notch or stopband filter 36 configured forrejecting transmit signal interference from the RF signal input from theantenna 16 via the receiver filter 26, a low noise amplifier (LNA) 38configured for amplifying the RF signal from the stop band filter 36with a relatively low noise, a tunable bandpass filter 40 configured foroutputting the amplified RF signal at a frequency selected by thecontroller/processor 14, and a downconverter 42 configured fordownconverting the RF signal to a baseband signal that is provided tothe controller/processor 14. Alternatively, the function of rejectingtransmit signal interference performed by the stop-band filter 36 caninstead be performed by the duplexer 18. Or, the power amplifier 34 ofthe transmitter 20 can be designed to reduce the transmit signalinterference.

It should be appreciated that the block diagram illustrated in FIG. 1 isfunctional in a nature, and that several functions can be performed byone electronic component or one function can be performed by severalelectronic components. For example, the functions performed by the upconverter 28, VGA 30, bandpass filter 40, downconverter 42, andcontroller/processor 14 are oftentimes performed by a single transceiverchip. The function of the bandpass filter 32 can be into the poweramplifier 34 and the transmit filter 24 of the duplexer 18.

Microwave filters are generally built using two circuit building blocks:a plurality of resonators, which store energy very efficiently at aresonant frequency (which may be a fundamental resonant frequency f₀ orany one of a variety of higher order resonant frequencies f₁-f_(n)); andcouplings, which couple electromagnetic energy between the resonators toform multiple reflection zeros providing a broader spectral response.For example, a four-resonator filter may include four reflection zeros.For the purposes of this specification, a reflection zero may refer tothe roots of a filter's reflection function where the inductance andcapacitance cancel and a minimum amount of power is reflected. Thestrength of a given coupling is determined by its reactance (i.e.,inductance and/or capacitance). The relative strengths of the couplingsdetermine the filter shape, and the topology of the couplings determineswhether the filter performs a band-pass or a band-stop function. Theresonant frequency f₀ is largely determined by the inductance andcapacitance of the respective resonator. For conventional filterdesigns, the frequency at which the filter is active is determined bythe resonant frequencies of the resonators that make up the filter. Eachresonator must have very low internal resistance to enable the responseof the filter to be sharp and highly selective for the reasons discussedabove. This requirement for low resistance tends to drive the size andcost of the resonators for a given technology.

The front-end receive filter (e.g., the receive filter 26 illustrated inFIG. 1) preferably takes the form of a sharply defined band-pass filterto eliminate various adverse effects resulting from strong interferingsignals at frequencies near the desired received signal frequency.Because of the location of the front-end receiver filter at the antennainput, the insertion loss must be very low so as to not degrade thenoise figure. In most filter technologies, achieving a low insertionloss requires a corresponding compromise in filter steepness orselectivity. In practice, most filters for cell phone handsets areconstructed using acoustic resonator technology, such as surfaceacoustic wave (SAW), bulk acoustic wave (BAW), and film bulk acousticresonator (FBAR) technologies. Such acoustic resonator filters have theadvantages of low insertion loss, compact size, and low cost compared toequivalent inductor/capacitor resonators.

Design of practical microwave filters may begin with the design of aninitial circuit generated, for instance, using image design or networksynthesis design. These approaches generally, from the outset, onlyconsider circuits with the fewest possible number of circuit elements.This is generally performed from a desire to minimize losses in thefinal filter, and may be a common practice in microwave filter design ofall types. The initial design may be generated using simplified,idealized circuit element models, which may typically ignore losses andother unwanted characteristics of the physical circuit elements used tomake the final filter. Computer optimization may be a critical andnecessary step in the design of practical microwave filters. Designtools including Agilent Advanced Design System (ADS), among others, mayuse numerical optimization methods, such as Monte Carlo, gradient, etc.,to improve the “initial circuit design.” This computer optimization stepmay use increasingly realistic, accurate circuit element models and mayrestrict circuit element values to those that can be manufactured inaccordance with the final filter design. The optimization may search forthe combination of circuit element values that best matches the desiredfilter response. This type of computer optimization may be often used inmicrowave filter design. Although the optimization may generally producea significantly improved design that may be realized with physicalcircuit elements, it generally does not reduce the number of circuitelements in the final circuit design from the number of circuit elementsin the initial circuit design, nor does it change one type of circuitelement into another.

For example, one initial circuit that is typically used in the design ofacoustic wave band-pass filters is a ladder filter 50, which comprises anumber of alternating shunt resonators 52 a and series resonators 52 b,as illustrated in FIG. 2. The filter 50 can be considered an N resonatorladder topology (i.e., N equals the number of resonators, and in thiscase 6). For the purposes of this specification, an acoustic ladderfilter may refer to one or more filters using the Mason-type acousticwave ladder circuit structure comprising alternating series and shuntacoustic wave resonators.

Each of the acoustic resonators 52 may be described by a modifiedButterworth-Van Dyke (MBVD) model 54. MBVD models 54 may also describeSAW resonators, which may be fabricated by disposing interdigitaltransducers (IDTs) on a piezoelectric substrate, such as crystallineQuartz, Lithium Niobate (LiNbO₃), Lithium Tantalate (LiTaO₃) crystals orBAW resonators. Each MBVD model 54 includes a motional capacitance C_(m)56, a static capacitance C₀ 58, a motional inductance L_(m) 60, and aresistance R 62. The motional capacitance C_(m) 56 and motionalinductance L_(m) 60 may result from the interactions of electrical andacoustical behavior, and thus, may be referred to as the motional arm ofthe MBVD model 54. The static capacitance C₀ 58 may result from theinherent capacitance of the structure, and thus, may be referred to asthe static (non-motional) capacitance of the MBVD model 54. Theresistance R 62 may result from the electrical resistance of theacoustic resonator 52. The parameters are related by the followingequations:

$\begin{matrix}{{\omega_{E} = \frac{1}{\sqrt{L_{m}C_{m}}}};} & \lbrack 1\rbrack \\{{\frac{\omega_{A}}{\omega_{R}} = \sqrt{1 + \frac{1}{\gamma}}},} & \lbrack 2\rbrack\end{matrix}$

where ω_(R) and ω_(A) may be the respective resonance and anti-resonancefrequencies for any given acoustic resonator, and gamma γ may depend ona material's property, which may be further defined by:

$\begin{matrix}{\frac{C_{0}}{C_{m}} = {\gamma.}} & \lbrack 3\rbrack\end{matrix}$

Typical γ values may range from about 12 to about 18 for 42-degree X Ycut LiTaO₃.

It can be appreciated from equation [1] that the resonant frequency ofeach of the acoustic resonators 52 will depend on the motional arm ofthe MBVD model 54, whereas the filter characteristics (e.g., bandwidth)will be determined by γ in equation [2]. The Quality factor (Q) for anacoustic resonator 52 may be an important figure of merit in acousticfilter design, relating to the loss of the element within the filter. Qof a circuit element represents the ratio of the energy stored per cycleto the energy dissipated per cycle. The Q factor models the real loss ineach acoustic resonator 52, and generally more than one Q factor may berequired to describe the loss in an acoustic resonator 52. Q factors maybe defined as follows for the filter examples. The motional capacitanceC_(m) 56 may have an associated Q defined as QC_(m)=1.0E+8; the staticcapacitance C₀ 58 may have an associated Q defined as QC₀=200; andmotional inductance L_(m) 60 may have an associated Q defined asQL_(m)=1000. Circuit designers may typically characterize SAW resonatorsby resonant frequency ω_(R), static capacitance C₀, gamma γ, and Qualityfactor QL_(m). For commercial applications, QL_(m) may be about 1000 forSAW resonators, and about 3000 for BAW resonators.

The frequency response for the filter 50 is illustrated in FIG. 3 whichpresents the scattering matrices |S21|² (insertion loss) and |S11|²(return loss) for the filter response in logarithmic units of decibels(dB) versus frequency f. Let the resonance and anti-resonancefrequencies of each of the shunt resonators 52 a be respectivelydesignated as ω_(rp) and ω_(ap), and the resonance and anti-resonancefrequencies of each of the series resonators 52 b be respectivelydesignated as ω_(rs) and ω_(as). When ω_(rs) and ω_(ap) areapproximately equal to each other, a passband centered near ω=ω_(rp),ω_(ap) is created, and transmission zeroes at ω=ω_(rp), ω_(as) definingthe passband edges are created, as shown in the filter responseillustrated in FIG. 3. For the purposes of this specification, atransmission zero may refer to the roots of a filter's transmissionfunction where a maximum amount of power is reflected. At frequencies ffar from the passband center frequency ω_(p) the resonators actapproximately as capacitors, resulting in a |S21|² filter response thatforms wings that becomes asymptotically constant for large |ω−ω_(p)|,providing the out-of-band rejection.

A band pass filter response may be characterized by the return loss(i.e., the value of the |S11|² at the center passband frequency ω_(p)),insertion loss (i.e., the value of |S21|² at the center passbandfrequency ω_(p), the passband width (PBW), and the out-of-bandrejections ε (i.e., 1/|S21| at a large |ω−ω_(p)|). Band pass ladderfilters can be designed only over a limited accessible range of theseparameters, with the range depending on the material parameter value γand the number of resonators (termed the filter order). The materialparameter values γ for currently widely used materials for SAW and BAWfilters are in the range of 12-14, allowing the resonance frequency andantiresonance frequency to be close to the passband center frequencyω_(p), thereby creating a relatively narrow passband in the |S21|²filter response. Materials with a material parameter value γ of 4 arecurrently under development. A smaller material parameter value γ wouldenable a wider passband width PBW, decrease return loss RL, or improvethe out-of-band rejection ε.

For a fixed passband width PBW, as the out-of-band rejection εincreases, the return loss RL decreases. In some cases, passive circuitelements are coupled to the ladder structure to improve filterperformance. For example, adding inductors can decrease the effectivematerial parameter value γ, which can increase the passband width PBW,decrease the return loss RL, or improve the out-of-band rejection ε.However, the benefits from the addition of inductors come at the cost ofincreased insertion loss, size, and cost. The band pass filterparameters are pushed to the limits of the accessible range in order tomaximize performance, with tradeoffs between the parameters depending onthe system applications and requirements. Higher order filters canachieve greater out-of-band rejection ε at a given passband return lossRL and passband width PBW.

As briefly discussed above, the filter 50 may have an initial circuitdesign, which may then be optimized via a suitable computer optimizationtechnique (e.g., Agilent ADS software) to create a final circuit design.For example, the filter 50 may initially be designed with the resonantfrequencies ω_(R) and static capacitances C₀ for each resonator 52illustrated in FIG. 4a , which when simulated, results in the frequencyresponse illustrated in FIG. 4b . This frequency response is showncharacterized by the following markers: M1 of Mag S21=−65.71 dB atfrequency=1.770 GHz; M2 of Mag S21=−36.735 dB at frequency=1.830 GHz; M3of Mag S21=−4.367 dB at frequency=1.850 GHz; M4 of Mag S21=−1.444 dB atfrequency=1.879 GHz; M5 of Mag S21=−2.680 dB at frequency=1.910 GHz; M6of Mag S21=−30.118 dB at frequency=1.930 GHz; and M7 of Mag S21=−62.874dB at frequency=1.990 GHz.

After optimization, the filter 50 may have the resonant frequenciesω_(R) and static capacitances C₀ for each resonator 52 illustrated inFIG. 5a , which when simulated, results in the frequency responseillustrated in FIG. 5b . This frequency response is shown characterizedby the following markers: N1 of Mag S21=−46.943 dB at frequency=1.770GHz; N2 of Mag S21=−29.865 dB at frequency=1.829 GHz; N3 of MagS21=−1.479 dB at frequency=1.851 GHz; N4 of Mag S21=−0.833 dB atfrequency=1.875 GHz; N5 of Mag S21=−1.898 dB at frequency=1.910 GHz; N6of Mag S21=−41.977 dB at frequency=1.929 GHz; and N7 of Mag S21=−47.182dB at frequency=1.990 GHz.

As can be appreciated from the foregoing, the values of the MBVD models54 for the resonators 52 have changed with optimization with improvementin the frequency response. However, the type and number of circuitelements remains unchanged, and thus, does not reduce the footprint orcost of the final circuit. Therefore, for microwave filters generally,and especially filter designs that contain passive elements and/or usemore complex design techniques, such as modern network theory or imagetheory with more complex sections, an improved optimization method isneeded.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings illustrate the design and utility of preferred embodimentsof the present invention, in which similar elements are referred to bycommon reference numerals. In order to better appreciate how theabove-recited and other advantages and objects of the present inventionsare obtained, a more particular description of the present inventionsbriefly described above will be rendered by reference to specificembodiments thereof, which are illustrated in the accompanying drawings.Understanding that these drawings depict only typical embodiments of theinvention and are not therefore to be considered limiting of its scope,the invention will be described and explained with additionalspecificity and detail through the use of the accompanying drawings inwhich:

FIG. 1 is a block diagram of a prior art wireless telecommunicationssystem;

FIG. 2 is a schematic diagram of a prior art acoustic ladder filter thatcan be used in the prior art wireless telecommunications system;

FIG. 3 is a frequency response plot of the prior art acoustic ladderfilter of FIG. 2;

FIG. 4a is a schematic diagram of an initial circuit design of theacoustic ladder filter of FIG. 2 that can be optimized using aconventional filter optimization technique;

FIG. 4b is a frequency response plot of the initial circuit design ofFIG. 4 a;

FIG. 5a is a schematic diagram of an optimized final circuit design ofthe acoustic ladder filter of FIG. 2 resulting from the optimization ofthe initial filter circuit design of FIG. 4a using the conventionalfilter optimization technique;

FIG. 5b is a frequency response plot of the final circuit design of FIG.5 a;

FIG. 6 is a flow diagram illustrating an Element Removal Design (ERD)technique used to optimize an acoustic ladder filter in accordance withone method of the present inventions;

FIG. 7a is a schematic diagram of an initial circuit design of anacoustic ladder filter that can be optimized using the ERD technique ofFIG. 6;

FIG. 7b is a frequency response plot of the initial circuit design ofFIG. 7 a;

FIG. 8a is a schematic diagram of an optimized final circuit designresulting from the optimization of the initial filter circuit design ofFIG. 7a using the ERD technique of FIG. 6;

FIG. 8b is a frequency response plot of the final circuit design of FIG.8a ; and

FIG. 9 is a block diagram of a computerized filter design system thatcan implement the computerized steps of the ERD technique of FIG. 6.

DETAILED DESCRIPTION OF THE EMBODIMENTS

The microwave filter design optimization technique optimizes an acousticwave (AW) microwave filter (such as surface acoustic wave (SAW), bulkacoustic wave (BAW), and film bulk acoustic wave (FBAR) filters), bychanging the circuit element values, changing the circuit element type,and/or discretely removing extra or unnecessary circuit elements. Theseelements may include inductors, capacitors, and acoustic resonators(modeled, e.g., using the modified Butterworth-Van Dyke (MBVD) model).

This optimization technique utilizes several traditional computeroptimization methods to enable the improved optimization of more complexcircuits in the initial design than may be possible in the prior art.These initial filter circuit designs may be produced using any designmethod, for instance image design or network synthesis. Thisoptimization technique results in a final filter circuit design with areduced number elements compared to the initial filter circuit design,while simultaneously improving the frequency response of the filter. Forthe purposes of this specification, a frequency response improvement mayrefer to an improvement in desired microwave performance of a filter(e.g., a lower insertion loss, steeper rejection slope, higherout-of-band rejection, lower node voltage, more linear group delay,etc.). Therefore, a smaller footprint, lower cost, lower insertion loss,and greater selectively filter may be achieved, while allowing the useof traditional manufacturing processes and infrastructure.

While the microwave filter design optimization technique is describedherein with reference to AW filters, it should be appreciated that thistechnique can be utilized with other types of microwave filters wherethe resonant elements can be model at some level of accuracy with a MBVDmodel. The optimization technique may also apply to other technologieswith complex resonator elements (e.g., multi-mode dielectric resonatorsand other similar technologies).

Referring now to FIG. 6, one Element Removal Design (ERD) technique 100that can be used to design an acoustic wave filter will be described.During implementation of the ERD technique 100, a design in process(DIP) is modified from an initial design to an improved final design.The method, in steps, uses computer optimization and decisions toincrementally improve the DIP to reduce circuit element count andimprove performance metrics.

To this end, the ERD technique 100 first generates an initial filtercircuit design based on performance specifications, such as centerpassband frequency, passband width, return loss, and out-of-bandrejection may be generated using and image filter technique or a networksynthesis technique (step 102). For the purposes of this specification,a circuit element may refer to an inductor, a capacitor, a resonator,switch or a resistor within a network of circuit interconnections.

For example, as shown in FIG. 7a , the initial filter circuit design maybe a band-pass ladder 200, which comprises a number of alternating shuntresonant elements 202 a and 202 b and series resonant elements 202 c. Inthe illustrated embodiment, each shunt leg of the ladder filter 200includes two parallel shunt resonant elements 202 a and 202 b that mayresonate at different frequencies. Each of the resonant elements 202 canbe modeled with the MBVD model 54 illustrated in FIG. 2. The ladderfilter 200 also comprises a plurality of non-resonant elements 204 inthe form of capacitors respectively associated with the series resonantelements 202 c. For the purposes of this specification, a non-resonantelement may refer to a passive component in a circuit. Exemplarynon-resonant elements may include inductors, capacitors, switches orresistors. Non-resonant elements may have resonances far from thefrequency of interest. For instance, an inductor may have a resonancegreater than 50% of the passband frequency. Thus, the filter 200includes nine resonant elements and three non-resonant elements.

The filter 200 may initially be designed with the resonant frequenciesω_(R) and static capacitances C₀ for each resonator 202 illustrated inFIG. 7a , which when simulated, results in the frequency responseillustrated in FIG. 7b . This frequency response is shown characterizedby the following markers: R1 of Mag S21=−24.627 dB at frequency=1.770GHz; R2 of Mag S21=−64.652 dB at frequency=1.830 GHz; R3 of MagS21=−3.857 dB at frequency=1.850 GHz; R4 of Mag S21=−0.987 dB atfrequency=1.881 GHz; R5 of Mag S21=−3.039 dB at frequency=1.910 GHz; R6of Mag S21=−87.468 dB at frequency=1.930 GHz; and R7 of Mag S21=−28.429dB at frequency=1.990 GHz. It is assumed that the circuit elements ofthe initial filter circuit design 200 have the following parameters:gamma γ=12, QC₀=200, Qcap=200, QL_(m)=1000, and Rs=0.5 ohms.

Next, the ERD technique 100 inputs the DIP (in this case the initialfilter design) into a computerized filter optimizer (e.g., Agilient ADS)(step 104). For the purposes of this specification, computeroptimization of a DIP may refer to improving the frequency response bychanging values of the circuit elements in a computer-based circuitsimulator. The circuit simulator may use goals in order to compare thesimulated response against a desired result. It should be appreciatedthat the DIP to be computer optimized is the initial circuit design atthis point, the ERD technique 100 may be implemented to improve a DIPduring any point of a filter design process. At any event, the resultingDIP has the same number of circuit elements as the number of circuitelements in the input DIP.

The ERD technique 100 then determines whether any of the non-resonantelements 204 in the DIP has become insignificant (“vanishes”) (step106). For the purposes of this specification, a circuit element tends tovanish if a series element reactance value and/or shunt elementsusceptance value becomes very small during computer optimization atstep 104 and/or the circuit element may be removed from a filter designwithout a significant impact on filter performance. A non-resonantelement 204 may tend to vanish according to its kind and placementwithin the filter circuit design.

For example, if the non-resonant element 204 is a series inductor or ashunt capacitor, it will tend to vanish as its absolute impedance valuebecomes small; for instance, less than 0.1 nH (inductor) or 0.1 pF(capacitor). In this case, the non-resonant element 204 will bedetermined to be insignificant if its absolute impedance value is lessthan the threshold value. In contrast, if the non-resonant element 204is a shunt inductor or a series capacitor, it will tend to vanish as itsabsolute impedance value becomes large; for instance, greater than 100nH (inductor) or 50 pF (capacitor). In this case, the non-resonantelement 204 will be determined to be insignificant if its absoluteimpedance value is greater than a threshold value.

As another example, a non-resonant element 204 will tend to vanish asits relative value (impedance or susceptance) becomes small (e.g., lessthan 10%) compared to other circuit elements of the same type (series orshunt) connected to them. Thus, if the non-resonant element 204 is aseries circuit element, it will be determined to be insignificant if apercentage of its absolute value relative to an absolute value ofanother series non-resonant element 204 in the DIP is less than athreshold value. Similarly, if the non-resonant element 204 is a shuntcircuit element, it will be determined to be insignificant if apercentage of its absolute value relative to an absolute value ofanother shunt non-resonant element 204 in the DIP is less than athreshold value.

As still another example, if the non-resonant element 204 is a seriescircuit element, it will tend to vanish as its impedance is less than apercentage (e.g., 10%) of the impedance seen in either direction fromthe non-resonant element 204. In this case, the non-resonant element 204will be determined to be insignificant if a percentage of the absoluteimpedance value of the non-resonant element 204 relative to an impedanceseen in either direction from the non-resonant element 204 is less thanthe threshold value. In contrast, if the non-resonant element 204 is ashunt circuit element, it will tend to vanish as its susceptance is lessthan a percentage (e.g., 10%) of the susceptance seen in eitherdirection from the non-resonant element 204. In this case, thenon-resonant element 204 will be determined to be insignificant if apercentage of the absolute susceptance value of the non-resonant element204 relative to a susceptance seen in either direction from thenon-resonant element 204 is less than the threshold value.

As yet another example, a non-resonant element 204 may tend to vanishwhen removing it results in less than a percentage degradation change(e.g., 10%) in a performance parameter of the filter circuit (e.g.,insertion loss, rejection slope, out-of-band rejection, node voltage,group delay flatness, etc.). In this case, the non-resonant element 204will be determined to be insignificant by removing the non-resonantelement 204 from the DIP if the value of the performance parameterwithout the non-resonant element 204 degrades the value of theperformance parameter with the non-resonant element 204 is less than athreshold value.

If it is determined that one of the non-resonant elements 204 in the DIPhas become insignificant at step 106, the ERD technique 100 determineswhether the sign of the insignificant non-resonant element 204 has beenpreviously changed (i.e., whether the non-resonant element 204 has beentransformed from an inductance to a capacitance, or from a capacitanceto an inductance) (step 108). Of course, in the case where DIP isgenerated for the first time, there will be no such previoustransformation.

Notably, the ERD technique 100 makes this inquiry to ensure that removalof the insignificant non-resonant element 204 is preferable overtransformation of the non-resonant element 204.

If the insignificant non-resonant element 204 has been previouslytransformed (indicating that the non-resonant element 204 vanished asboth a capacitor and an inductor) at step 108, the ERD technique 100generates a reduced filter circuit design by removing the insignificantnon-resonant element 204 from the DIP (step 110). If the non-resonantelement 204 has not been previously transformed (indicating that thenon-resonant element 204 vanished as one of a capacitance and aninductance, but not yet as the other of the capacitance and inductance)at step 108, the ERD technique 100 modifies the DIP by changing the signof the non-resonant element 204 (i.e., changing it from a capacitance toan inductance) (to the extent that the non-resonant element 204 isinitially a capacitance) or from an inductance to a capacitance (to theextent that the non-resonant element 204 is initially a capacitance))(step 112).

The ERD technique 100 then returns to step 104 to again optimize the DIPby inputting either the reduced filter circuit design generated in step110 or the transformed filter circuit design generated in step 112 intothe computerized filter optimizer, and then determines whether any ofthe remaining non-resonant elements 204 in the DIP has becomeinsignificant at step 108. If it is determined that one of thenon-resonant elements 204 in the DIP has become insignificant, the ERDtechnique again determines if the insignificant non-resonant element 204has been previously transformed at step 108. In the case where theinsignificant non-resonant element 204 has been previously transformed,then it is deemed that the insignificant non-resonant element 204 shouldhave been removed from previous DIP, and thus, it is removed at step110. In the case where the insignificant non-resonant element 204 hasnot been previously transformed, then the ERD technique 100 changes itat step 112.

If it is determined that none of the non-resonant elements 204 in theDIP (whether it is the first or a subsequently generated DIP) has becomeinsignificant at step 106, the ERD technique then determines whether anyof the resonant elements 202 in the DIP has become insignificant(“vanishes”) (step 114). A resonant element 202 may tend to vanish whenthe associated transmission zero associated with the resonant element202 is relatively far from all passbands and stopbands; for instance,when the resonant frequency ω_(R) and anti-resonant frequency ω_(A), asgiven in equations [1] and [2], move to more than 10% from the edgefrequency of the nearest passband or stopband.

If it is determined that one of the resonant elements 202 in the DIP hasbecome insignificant at step 114, the ERD technique modifies the DIP byreplacing the insignificant resonant element 202 with a staticcapacitance C₀, which preferably has a value equal to the value of thestatic capacitance of the insignificant resonant element 202 (step 116).Notably, a resonant element 202 that becomes insignificant will stillaffect the circuit because of its static capacitance, and so is betterreplaced by a capacitor than removed.

The ERD technique 100 then returns to step 104 to again optimize the DIPand then determines again whether any of the non-resonant elements 204in the DIP (including any static capacitance C₀ transformed from aninsignificant resonant element 202) has become insignificant at step106.

If it is determined that one of the non-resonant elements 204 in the DIPhas become insignificant, the ERD technique again determines if theinsignificant non-resonant element 204 has been previously transformedat step 108 and proceeds as discussed above. In the case where theinsignificant non-resonant element 204 is a static capacitance C₀ thathas replaced an insignificant resonant element 202, then it is confirmedthat the insignificant circuit element (which previously was a resonantelement 202, but is now a non-resonant element 204) should be entirelyremoved, and thus, is so removed at step 110.

If it is determined that at step 106 that none of the non-resonantelements 204 in the DIP has become insignificant, the ERD technique 100again determines whether any of the resonant elements 202 in the DIP hasbecome insignificant at step 114. If it is determined that one of theresonant elements 202 in the DIP has become insignificant, the ERDtechnique replaces the insignificant resonant element 202 with a staticcapacitance C₀ at step 116, and proceeds as discussed above.

If it determined that none of the resonant elements 202 in the DIP hasbecome insignificant, the ERD technique 100 deems the DIP to be theimproved final filter circuit design (step 118), which in the exemplaryembodiment, has the resonant frequencies ω_(R) and static capacitancesC₀ for the remaining resonant elements 202 and non-resonant elements 204illustrated in FIG. 8a , which when simulated, results in the frequencyresponse illustrated in FIG. 8b . This frequency response is showncharacterized by the following markers: P1 of Mag S21=−30.080 dB atfrequency=1.770 GHz; P2 of Mag S21=−34.193 dB at frequency=1.830 GHz; P3of Mag S21=−1.394 dB at frequency=1.850 GHz; P4 of Mag S21=−0.761 dB atfrequency=1.872 GHz; P5 of Mag S21=−1.406 dB at frequency=1.910 GHz; P6of Mag S21=−45.227 dB at frequency=1.930 GHz; and P7 of Mag S21=−45.227dB at frequency=1.990 GHz.

As can be seen from a comparison between FIG. 7a and FIG. 8a , theimproved final filter circuit design includes fewer circuit elements,and in particular, two less resonant elements 202 and one lessnon-resonant element 204. As can be seen from a comparison between FIG.8a and FIG. 8b , the final filter circuit design yields a flatterfrequency response and loss at the pass-band. It should also be notedthat a conventional optimization technique (i.e., without removingcircuit elements) was performed on the initial filter circuit 200illustrated in FIG. 7a , resulting in a final filter circuit having afrequency response performance that was not as good as the frequencyresponse performance yield by the ERT technique illustrated in FIG. 8b .Thus, contrary to conventional wisdom, the removal of circuit elementsusing the ERT technique not only decreased the cost and size of themicrowave filter, it improves the frequency response performance of themicrowave filter over prior art microwave filters that have more circuitelements.

Notably, the ERD technique 100 may analyze the frequency response of DIPresulting from step 104 in order to determine whether a previous stepshould be undone or redone.

For example, if the frequency response performance of the DIP is notbetter than the frequency response performance of the initial filtercircuit design, this means that the initial filter circuit design is notacceptable, and thus, a different initial filter circuit design may beconsidered, which may then be inputted into the computerized filteroptimizer at step 104.

As another example, if the frequency response performance of the DIP asit existed after a non-resonant element 204 has been transformed (from acapacitance to an inductance, or from an inductance to a capacitance) isworse by a threshold amount relative to the frequency responseperformance of the DIP as it existed before the non-resonant element 204was transformed, the ERD technique 100 may simply return to the previousDIP and remove the non-resonant element 204 from that design.

As still another example, if the frequency response performance of theDIP as it existed after a resonant element 202 has been transformed intoa static capacitance C₀ is worse by a threshold amount relative to thefrequency response performance of the DIP as it existed before theresonant element 202 was transformed, the ERD technique may simplyreturn to the previous DIP and restore the resonant element 204 backinto that design.

Once the improved final filter circuit design is achieved, the ERDtechnique 100 manufactures an actual microwave filter based on the finalfilter circuit design (step 120). Preferably, the circuit element valuesof the actual microwave filter will match the corresponding circuitelement values in the improved final filter circuit design.

Referring first to FIG. 9, a computerized filter design system 300 maybe used to design a microwave filter using the ERD technique 100. Thecomputerized filter design system 300 generally comprises a userinterface 302 configured for receiving information and data from a user(e.g., parameter values and filter specifications) and outputting anoptimized filter circuit design to the user; a memory 304 configured forstoring filter design software 308 (which may take the form of softwareinstructions, which may include, but are not limited to, routines,programs, objects, components, data structures, procedures, modules,functions, and the like that perform particular functions or implementparticular abstract data types), as well as the information and datainput from the user via the user interface 302; and a processor 306configured for executing the filter design software. The filter designsoftware program 308 is divided into sub-programs, in particular, aconventional network design synthesizer 310 (which can be used togenerate the initial filter circuit design at step 102), a conventionalfilter optimizer 312 (which can be used to generate the DIP at step104), and an element removal design engine 314 that controls the networkdesign synthesizer 88 and filter optimizer 90 in accordance with filtercircuit design aspects of the ERD technique 100 in order to generate theoptimized final circuit design.

Although particular embodiments of the present invention have been shownand described, it should be understood that the above discussion is notintended to limit the present invention to these embodiments. It will beobvious to those skilled in the art that various changes andmodifications may be made without departing from the spirit and scope ofthe present invention. For example, the present invention hasapplications well beyond filters with a single input and output, andparticular embodiments of the present invention may be used to formduplexers, multiplexers, channelizers, reactive switches, etc., wherelow-loss selective circuits may be used. Thus, the present invention isintended to cover alternatives, modifications, and equivalents that mayfall within the spirit and scope of the present invention as defined bythe claims.

1. (canceled)
 2. A method for generating a model of a reduced componentnarrowband acoustic wave microwave filter, comprising: initializing, bya processor of a computing system, a first filter circuit model based onone or more performance specifications, the first filter circuit modelcomprising a plurality of circuit elements, wherein the plurality ofcircuit elements comprises a plurality of resonant elements and one ormore non-resonant elements; for each of one or more circuit elements:determining a significance of the circuit element, by the processor,based on one of a comparison of an impedance of the circuit element to athreshold value, or comparison of a resonant frequency of the circuitelement to a passband or stopband of the one or more performancespecifications, and removing the circuit element from the first filtercircuit model, by the processor, responsive to the determinationindicating a lack of significance; and generating, by the processor, asecond filter circuit model comprising a subset of the plurality ofcircuit elements that were not removed.
 3. The method of claim 2,wherein a first circuit element is a series inductor or shunt capacitor;and wherein determining a significance of the first circuit elementcomprises determining that the first circuit element lacks significanceresponsive to an absolute impedance of the first circuit element beingless than the threshold value.
 4. The method of claim 2, wherein a firstcircuit element is a series capacitor or shunt inductor; and whereindetermining a significance of the first circuit element comprisesdetermining that the first circuit element lacks significance responsiveto an absolute impedance of the first circuit element being greater thanthe threshold value.
 5. The method of claim 2, wherein a first circuitelement is a resonant element.
 6. The method of claim 5, where removingthe first circuit element comprises replacing the first circuit elementwith a capacitor in the first filter circuit model.
 7. The method ofclaim 2, wherein a first circuit element is a non-resonant element. 8.The method of claim 7, wherein removing the first circuit elementcomprises one of: replacing the first circuit element with an equivalentcapacitive element, responsive to the first circuit element comprisingan inductive element; or replacing the first circuit element with anequivalent inductive element, responsive to the first circuit elementcomprising a capacitive element.
 9. The method of claim 8, furthercomprising determining a significance of the replaced first circuitelement, based on one of the comparison of the impedance of the replacedfirst circuit element to the threshold value, or comparison of theresonant frequency of the replaced first circuit element to the passbandor stopband of the one or more performance specifications.
 10. Themethod of claim 8, wherein the equivalent capacitive element has a valueequal to a value of a static capacitance of the first circuit element.11. The method of claim 7, wherein removing the first circuit elementfrom the first filter circuit model further comprises: determining thatthe first circuit element has previously been transformed betweencapacitive and inductive elements; and removing the first circuitelement, responsive to the determination that the first circuit elementhas previously been transformed between capacitive and inductiveelements.
 12. A system for generating a model of a reduced componentnarrowband acoustic wave microwave filter, comprising: a processorexecuting a network design synthesizer and an element removal designengine; wherein the network design synthesizer is configured to:initialize a first filter circuit model based on one or more performancespecifications, the first filter circuit model comprising a plurality ofcircuit elements, wherein the plurality of circuit elements comprises aplurality of resonant elements and one or more non-resonant elements;and wherein the element removal design engine is configured to: for eachof one or more circuit elements: determine a significance of the circuitelement, based on one of a comparison of an impedance of the circuitelement to a threshold value, or comparison of a resonant frequency ofthe circuit element to a passband or stopband of the one or moreperformance specifications, and remove the circuit element from thefirst filter circuit model, responsive to the determination indicating alack of significance; and generate a second filter circuit modelcomprising a subset of the plurality of circuit elements that were notremoved.
 13. The system of claim 12, wherein a first circuit element isa series inductor or shunt capacitor; and wherein the element removaldesign engine is further configured to determine that the first circuitelement lacks significance responsive to an absolute impedance of thefirst circuit element being less than the threshold value.
 14. Thesystem of claim 12, wherein a first circuit element is a seriescapacitor or shunt inductor; and wherein the element removal designengine is further configured to determine that the first circuit elementlacks significance responsive to an absolute impedance of the firstcircuit element being greater than the threshold value.
 15. The systemof claim 12, wherein a first circuit element is a resonant element. 16.The system of claim 15, where wherein the element removal design engineis further configured to replace the first circuit element with acapacitor in the first filter circuit model.
 17. The system of claim 12,wherein a first circuit element is a non-resonant element.
 18. Thesystem of claim 17, wherein the element removal design engine is furtherconfigured to either: replace the first circuit element with anequivalent capacitive element, responsive to the first circuit elementcomprising an inductive element, or replace the first circuit elementwith an equivalent inductive element, responsive to the first circuitelement comprising a capacitive element.
 19. The system of claim 18,wherein the element removal design engine is further configured todetermine a significance of the replaced first circuit element, based onone of the comparison of the impedance of the replaced first circuitelement to the threshold value, or comparison of the resonant frequencyof the replaced first circuit element to the passband or stopband of theone or more performance specifications.
 20. The system of claim 18,wherein the equivalent capacitive element has a value equal to a valueof a static capacitance of the first circuit element.
 21. The system ofclaim 17, wherein the element removal design engine is furtherconfigured to: determine that the first circuit element has previouslybeen transformed between capacitive and inductive elements; and removethe first circuit element, responsive to the determination that thefirst circuit element has previously been transformed between capacitiveand inductive elements.